A331602 a(1) = 0; for n > 1, a(n) = A007947(A156552(n)).

0, 1, 2, 3, 2, 5, 2, 7, 6, 3, 2, 11, 2, 17, 10, 15, 2, 13, 2, 19, 6, 33, 2, 23, 6, 65, 14, 35, 2, 21, 2, 31, 34, 129, 10, 3, 2, 257, 66, 39, 2, 37, 2, 67, 22, 57, 2, 47, 6, 5, 130, 131, 2, 29, 6, 71, 258, 205, 2, 43, 2, 2049, 38, 21, 34, 69, 2, 259, 514, 41, 2, 55, 2, 4097, 26, 515, 10, 133, 2, 79, 30, 8193, 2, 15, 66, 16385, 114, 15, 2, 15, 6, 1027, 410, 10923

Offset: 1

Author

Antti Karttunen, Jan 22 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000035, A007947, A156552.

Cf. also A322993.

Programs

Mathematica

Array[Times @@ FactorInteger[#][[All, 1]] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]] &, 94] (* Michael De Vlieger, Jan 24 2020 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]);
A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A331602(n) = A007947(A156552(n));

Formula

a(1) = 0; and for n > 1, a(n) = A007947(A156552(n)).

A000035(a(n)) = 1 - A000035(n). [Flips the parity]